EMTH210-20S1 (C) Semester One 2020

Engineering Mathematics 2

15 points

Details:
Start Date: Monday, 17 February 2020
End Date: Sunday, 21 June 2020
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Friday, 28 February 2020
  • Without academic penalty (including no fee refund): Friday, 29 May 2020

Description

This course covers material in multivariable integral and differential calculus, linear algebra and statistics which is applicable to the engineering professions.

Mathematics underpins almost every aspect of modern engineering. This is reflected by the fact that all first professional year students must take EMTH210. With the centrality of this course to your professional development in mind, considerable effort has gone into selecting mathematical and statistical topics which will provide the groundwork for you to appropriately mathematise your engineering work. Throughout the course, your lecturers will also endeavour to relate the rigour of the mathematics to the practicality of the situations in which it will be applied, as we concentrate on your ability to apply the techniques to realistic situations.

The following topics will be covered, subject to the time available:
• Partial differentiation, chain rule, gradient, directional derivatives, tangent planes, Jacobian, differentials, line integrals, divergence and curl, extreme values and Lagrange multipliers.
• Second order linear differential equations and their applications.
• Fourier series.
• Double and triple integrals: elements of area, change of order of integration, polar coordinates, volume elements, cylindrical and spherical coordinates.
• Eigenvalues and eigenvectors and their applications.
• Laplace transforms.
• Statistics: approximating expectations, characteristic functions, random vectors (joint distributions, marginal distributions, expectations, independence, covariance), linking data to probability models (sample mean and variance, order statistics and the empirical distribution function, convergence of random variables, law of large numbers and point estimation, the central limit theorem, error bounds and confidence intervals, sample size calculations, likelihood).

Learning Outcomes

  • A student achieving total mastery of this course will be able to:
  • Show proficiency in multivariable calculus, including partial differentiation, implicit partial differentiation, the multidimensional chain rule, gradient, directional derivative, tangent planes, Jacobians, differentials, line integrals (exact and inexact), divergence, curl, and Lagrange multipliers.
  • Solve homogeneous constant coefficient ODEs and also inhomogeneous constant coefficient ODEs using undetermined coefficients.   This includes ODEs of order other than two.
  • Solve elementary second order boundary value problems, and appreciate some applications of BVPs in engineering.
  • Calculate real Fourier series of arbitrary period, and employ them to solve ODEs with periodic driving functions.  The student will also be knowledgeable of concepts such as harmonics and Gibbs phenomenon in Fourier series analysis.
  • Integrate in multiple dimensions using Cartesian, polar and spherical polar coordinate systems.  
  • Calculate the eigenpairs of matrices.
  • Familiar with orthogonal decomposition, and use it to find the principal axes of an ellipse.
  • Proficient in the solution of systems of first and second order ODEs via eigenvalues and eigenvectors, and familiar with the implications defective matrices in such situations.
  • Apply Laplace transforms to differential and some integral equations, including those with piecewise functions via the Heaviside step function.
  • Approximate expectations.
  • Work with random vectors, joint and marginal distributions, independence and covariance.
  • Link data to probability models, sample mean, variance, order statistics, and the empirical distribution function.
  • Be familiar with convergence of random variables, the law of large numbers, point estimation, the central limit theorem, likelihood, error bounds, and confidence intervals.
  • Do sample size calculations.

Pre-requisites

Subject to approval of the Dean of Engineering and Forestry

Restrictions

EMTH202, EMTH204, MATH201, MATH261, MATH262, MATH264

Timetable 2020

Students must attend one activity from each section.

Lecture A
Activity Day Time Location Weeks
01 Monday 08:00 - 09:00 - (23/3, 20/4)
Online Delivery (4/5-25/5)
C1 Lecture Theatre (17/2-16/3)
17 Feb - 29 Mar
20 Apr - 26 Apr
4 May - 31 May
02 Monday 12:00 - 13:00 - (23/3, 20/4)
Online Delivery (4/5-25/5)
C1 Lecture Theatre (17/2-16/3)
17 Feb - 29 Mar
20 Apr - 26 Apr
4 May - 31 May
Lecture B
Activity Day Time Location Weeks
01 Tuesday 09:00 - 10:00 - (24/3, 21/4)
Online Delivery (28/4-26/5)
C1 Lecture Theatre (18/2-17/3)
17 Feb - 29 Mar
20 Apr - 31 May
02 Tuesday 12:00 - 13:00 - (24/3, 21/4)
Online Delivery (28/4-26/5)
C1 Lecture Theatre (18/2-17/3)
17 Feb - 29 Mar
20 Apr - 31 May
Lecture C
Activity Day Time Location Weeks
01 Wednesday 08:00 - 09:00 - (25/3, 22/4)
Online Delivery (29/4-27/5)
C1 Lecture Theatre (19/2-18/3)
17 Feb - 29 Mar
20 Apr - 31 May
02 Wednesday 12:00 - 13:00 - (25/3, 22/4)
Online Delivery (29/4-27/5)
A1 Lecture Theatre (19/2-18/3)
17 Feb - 29 Mar
20 Apr - 31 May
Lecture D
Activity Day Time Location Weeks
01 Thursday 10:00 - 11:00 - (23/4-28/5)
C1 Lecture Theatre (20/2-19/3)
17 Feb - 22 Mar
20 Apr - 31 May
02 Thursday 14:00 - 15:00 - (23/4-28/5)
C1 Lecture Theatre (20/2-19/3)
17 Feb - 22 Mar
20 Apr - 31 May
Tutorial A
Activity Day Time Location Weeks
01 Wednesday 13:00 - 14:00 17 Feb - 29 Mar
20 Apr - 31 May
02 Thursday 09:00 - 10:00 17 Feb - 22 Mar
20 Apr - 31 May
03 Friday 12:00 - 13:00 17 Feb - 22 Mar
20 Apr - 31 May
05 Friday 15:00 - 16:00 17 Feb - 22 Mar
20 Apr - 31 May
06 Tuesday 14:00 - 15:00 17 Feb - 29 Mar
20 Apr - 31 May
08 Monday 09:00 - 10:00 17 Feb - 29 Mar
20 Apr - 26 Apr
4 May - 31 May
09 Friday 13:00 - 14:00 17 Feb - 22 Mar
20 Apr - 31 May
10 Monday 13:00 - 14:00 17 Feb - 29 Mar
20 Apr - 26 Apr
4 May - 31 May
12 Wednesday 11:00 - 12:00 17 Feb - 29 Mar
20 Apr - 31 May
13 Thursday 16:00 - 17:00 17 Feb - 22 Mar
20 Apr - 31 May
14 Thursday 11:00 - 12:00 17 Feb - 22 Mar
20 Apr - 31 May
15 Tuesday 16:00 - 17:00 17 Feb - 29 Mar
20 Apr - 31 May
16 Thursday 13:00 - 14:00 17 Feb - 22 Mar
20 Apr - 31 May
17 Tuesday 13:00 - 14:00 17 Feb - 29 Mar
20 Apr - 31 May
18 Monday 15:00 - 16:00 17 Feb - 29 Mar
20 Apr - 26 Apr
4 May - 31 May
20 Wednesday 14:00 - 15:00 17 Feb - 29 Mar
20 Apr - 31 May
22 Monday 10:00 - 11:00 17 Feb - 29 Mar
20 Apr - 26 Apr
4 May - 31 May
23 Thursday 10:00 - 11:00 17 Feb - 22 Mar
20 Apr - 31 May
24 Monday 16:00 - 17:00 17 Feb - 29 Mar
20 Apr - 26 Apr
4 May - 31 May
25 Monday 13:00 - 14:00 17 Feb - 29 Mar
20 Apr - 26 Apr
4 May - 31 May
26 Wednesday 15:00 - 16:00 17 Feb - 29 Mar
20 Apr - 31 May
27 Friday 14:00 - 15:00 17 Feb - 22 Mar
20 Apr - 31 May
28 Friday 10:00 - 11:00 17 Feb - 22 Mar
20 Apr - 31 May
29 Tuesday 10:00 - 11:00 17 Feb - 29 Mar
20 Apr - 31 May
30 Tuesday 15:00 - 16:00 17 Feb - 29 Mar
20 Apr - 31 May
31 Tuesday 09:00 - 10:00 17 Feb - 29 Mar
20 Apr - 31 May
32 Wednesday 13:00 - 14:00 17 Feb - 29 Mar
20 Apr - 31 May
33 Friday 09:00 - 10:00 17 Feb - 22 Mar
20 Apr - 31 May
34 Monday 11:00 - 12:00 17 Feb - 29 Mar
20 Apr - 26 Apr
4 May - 31 May
35 Thursday 14:00 - 15:00 17 Feb - 22 Mar
20 Apr - 26 Apr
4 May - 31 May
36 Wednesday 10:00 - 11:00 17 Feb - 29 Mar
20 Apr - 31 May
37 Monday 12:00 - 13:00 17 Feb - 29 Mar
20 Apr - 26 Apr
4 May - 31 May

Examination and Formal Tests

Test A
Activity Day Time Location Weeks
01-P1 Wednesday 12:00 - 00:00 27 Apr - 3 May
01-P2 Thursday 07:00 - 12:00 27 Apr - 3 May

Course Coordinator

For further information see Mathematics and Statistics Head of Department

Assessment

To pass the course, there is a minimum mark required in the Final Examination of 40%, as well as achieving 50% or more in total across all the assessments.

Textbooks / Resources

Recommended Reading:
•“Advanced Engineering Mathematics” by Erwin Kreyszig. (This text also covers the statistics material.)
•“Advanced Engineering Mathematics” by Zill and Wright.
•“Advanced Engineering Mathematics” by Zill and Cullen.

Indicative Fees

Domestic fee $975.00

International fee $5,500.00

* Fees include New Zealand GST and do not include any programme level discount or additional course related expenses.

For further information see Mathematics and Statistics.

All EMTH210 Occurrences

  • EMTH210-20S1 (C) Semester One 2020